Question

A sample was done, collecting the data below . Calculate the standard deviation , to one decimal place. 30 6 1 3 8

Answer 1

Given:

Given data is 30, 6, 1, 3, 8.

Required:

To find the standard deviation of the given data set.

Explanation:

The formula for standard deviation is,

$\sigma=\sqrt{\frac{1}{N}(\sum_{i=1}^N}(xi-x)^2$

Here

$\begin{gathered} N=5 \\ x=\frac{30+6+1+3+8}{5} \\ \\ x=9.6 \end{gathered}$

Now

$\begin{gathered} \sigma=\sqrt{\frac{1}{5}}(30-9.6)^2+...(8-9.6)^2 \\ \\ =\sqrt{\frac{1}{5}(416.16+12.96+73.96+43.56+2.56} \\ \\ =\sqrt{\frac{549.2}{5}} \\ \\ =\sqrt{109.84} \\ \\ =10.48 \\ \\ \sigma=10.5 \end{gathered}$

Final Answer:

The standard deviation of the given data set is 10.5